HillSaturation

class pymc_marketing.mmm.components.saturation.HillSaturation(priors=None, prefix=None)

Wrapper around Hill saturation function.

Multiplies pymc_marketing.mmm.transformers.hill_function() by an extra scaling parameter beta so the curve can reach an asymptote other than 1.

Parameters:

slopetensor

Slope of the Hill curve, controlling its steepness. Default prior: Prior("HalfNormal", sigma=1.5).

kappatensor

Half-saturation point where the response equals half its asymptote. Default prior: Prior("HalfNormal", sigma=1.5).

betatensor

Asymptote that the saturated response approaches as the input grows. Default prior: Prior("HalfNormal", sigma=1.5).

.. plot::

context:

close-figs

import matplotlib.pyplot as plt import numpy as np from pymc_marketing.mmm import HillSaturation

rng = np.random.default_rng(0)

adstock = HillSaturation() prior = adstock.sample_prior(random_seed=rng) curve = adstock.sample_curve(prior) adstock.plot_curve(curve, random_seed=rng) plt.show()

Methods

HillSaturation.__init__([priors, prefix])
HillSaturation.apply(x, *[, dims, core_dim, idx])	Call within a model context.
HillSaturation.from_dict(data)	Reconstruct a saturation transformation from a dict.
HillSaturation.function(x, slope, kappa, beta, *)	Hill saturation function.
HillSaturation.plot_curve(curve[, ...])	Plot curve HDI and samples.
HillSaturation.plot_curve_hdi(curve[, ...])	Plot the HDI of the curve.
HillSaturation.plot_curve_samples(curve[, ...])	Plot samples from the curve.
HillSaturation.sample_curve([parameters, ...])	Sample the curve of the saturation transformation given parameters.
HillSaturation.sample_prior([coords])	Sample the priors for the transformation.
HillSaturation.set_dims_for_all_priors(dims)	Set the dims for all priors.
HillSaturation.to_dict([_orig])	Convert the transformation to a dictionary.
HillSaturation.update_priors(priors)	Update the priors for a function after initialization.
HillSaturation.with_default_prior_dims(dims)	Return a copy with default prior dims (dims=None) set to dims instead.
HillSaturation.with_updated_priors(priors)	Return a copy with updated priors.

Attributes

combined_dims	Get the combined dims for all the parameters.
default_priors
function_priors	Get the priors for the function.
model_config	Mapping from variable name to prior for the model.
prefix
priors	Get the priors for the function.
variable_mapping	Mapping from parameter name to variable name in the model.